~~NOTOC~~
======  Thickness & LET assignment ======
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===== Data exploration =====
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Raster plot of Measurements.\\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:measurements_matrix.pdf}}


Data plots.\\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:preliminary_data_plots.pdf }}


Residual plots (after LS-fitting of a 6-parameter polynomial surface). \\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:preliminary_residual_plots.pdf }}


Raster plot of residuals.\\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:residuals_matrix.pdf }}


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===== Variogram  exploration and estimation =====
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"Cloud" empirical variogram, both classical and robust algorithms.\\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:cloud_empirical_variogram.pdf}}


Box-plots from "Cloud" empirical variograms.\\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:boxplot_cloud_empirical_variogram.pdf}}

Empirical variogram.\\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:empirical_variogram.pdf}}

Empirical and kernel-smoothed variogram.\\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:empirical_and_kernel-smoothed_variogram.pdf}}

Estimated directional variograms.\\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:estimated_directional_variograms.pdf}}

W-LS parametric fits for the estimated variogram.\\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:fitted_variograms.pdf}}


\\
===== Preliminary Kriging prediction of the thickness map =====
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Universal Kriging algorithm, with second order polynomial trend surface and using a spherical function fit of the omnidirectional variogram.


Estimation of the missing samples (interpolation on original (x,y) grid, 25x25 points).\\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:uk_missingpoints-matrixplot.pdf}}

Estimation of values outside the original measurement (x,y) grid (extrapolation).\\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:uk_extrap-matrixplot.pdf}}

Estimation on a 52x52 points grid.\\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:uk_detailed_grid_52x52-matrixplot.pdf}}

Estimation on a grid with 75x75 points.\\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:uk_detailed_grid_-75x75_-matrixplot.pdf}}

Estimation on a grid with 100x100 points.\\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:uk_detailed_grid_-100x100_-matrixplot.pdf}}

Estimation on a grid with 150x150 points.\\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:uk_detailed_grid_-150x150_-matrixplot.pdf}}

Estimation on a grid with 200x200 points.\\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:uk_detailed_grid_-200x200_-matrixplot.pdf}}


//Prediction std. error (sq. root of Kriging prediction variance)//. \\
Maximum value: max(sqrt(uk_detailed$krige.var)) =  0.00173101  [mm].\\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:kriging_std_error.pdf }}

//Cross-Validation//. \\
"Leaving-one-out" cross-validation method, where each data location is removed from
the data set and the variable at this location is predicted using the remaining locations, for the given
model. This was for all of the data locations. \\
{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:cross-validation.pdf }}





Animated GIF pictures with rotations of the 200x200 UK-interpolated surface. There are some pics available in the Media Manager section of the wiki. \\

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{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:movie-axis1.gif }}

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{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:movie-axis2.gif }}

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{{data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging-preliminary:movie-axis3.gif }}




